I saw some time ago a post discussing the issues surrounding encryption of speech/voice in VoIP and how it can leak information (can't find it now). Can someone provide an insight into some of the issues and how to mitigate them if one wants to use symmetric encryption to encrypt voice between two devices? Is asymmetric encryption possible (give the processing time required)?

2 Answers
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I'm not sure which post you're referring to, but one possible source of leakage results from using a variable-bit rate codec. If different sounds compress at different rates, than this will be reflected in the lengths of outgoing encrypted packets. By examining those sequences of lengths, it can sometimes be possible to accurately guess what phrases are being uttered.

Padding the ciphertext packets, to, say, the nearest multiple of 128 or 256 bits can greatly reduce the ability of an attacker to make this type of attack. I would assume that using a non-variable bit rate codec would also work. Of course, there's a trade-off with bandwidth here; you'd have to weigh that against the security risks.

I strongly suspect assymetric crypto is not fast enough for the job. Typically, it's just used to establish a secure, authenticated channel so that users can agree on a symmetric key, which is used to encrypt the actual traffic.

Performing type of attack---looking at lengths, timings, etc. to infer information about content---is called traffic analysis.